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<a href="tensor_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef TENSOR_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define TENSOR_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//#include &lt;math.h&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">//Forward declaration</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00010"></a><span class="lineno"><a class="line" href="class_tensor.html">   10</a></span>&#160;  <span class="keyword">class </span><a class="code" href="class_tensor.html">Tensor</a>;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> * First-order Tensor class</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00017"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">   17</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_tensor.html">Tensor</a> &lt;1,dim,T&gt; {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  <a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor</a>();</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  <a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor</a>(<span class="keyword">const</span> <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> &amp;b);</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment"> * Access/set an element of the tensor.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#acc931891ae9e3bb537e3a0a78ff87d8f">   25</a></span>&#160;  T&amp; <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#acc931891ae9e3bb537e3a0a78ff87d8f">operator[]</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i){ <span class="keywordflow">return</span> <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i]; };</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment"> * Access an element of the tensor.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#a326179f24c05ffe25beedd71ff0f23b1">   30</a></span>&#160;  <span class="keyword">const</span> T&amp; <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#a326179f24c05ffe25beedd71ff0f23b1">operator[]</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i]; };</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a>&amp; <a class="code" href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">operator=</a>(<span class="keyword">const</span> <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> &amp;b);</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  T norm() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  </div>
<div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aec326c324745d11291d2f0d5d7eea804">   34</a></span>&#160;  std::vector&lt;T&gt; <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aec326c324745d11291d2f0d5d7eea804">value</a>;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;};</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment"> * Default constructor.</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#a09dacbd79d16b74ba8698e27ae3dc42b">   41</a></span>&#160;<a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor&lt;1,dim,T&gt;::Tensor</a>() : value(dim){}</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment"> * Copy constructor.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#ae497a4c79545b71c83089a8a33561cc9">   47</a></span>&#160;<a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor&lt;1,dim,T&gt;::Tensor</a>(<span class="keyword">const</span> <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> &amp;b){</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  *<span class="keyword">this</span> = b;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  </div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;}</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="comment"> * Assignment operator.</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#a8973e023404c6e377bf658ee712c2210">   57</a></span>&#160;<a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a>&amp; <a class="code" href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">Tensor&lt;1,dim,T&gt;::operator=</a>(<span class="keyword">const</span> <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> &amp;b){</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a> = b.<a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aec326c324745d11291d2f0d5d7eea804">value</a>;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;}</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment"> * Compute the L2-norm of a 1st order tensor.</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aa4e16153f772c2deed7110f8f4b00dd0">   68</a></span>&#160;T <a class="code" href="class_tensor.html">Tensor&lt;1,dim,T&gt;::norm</a>()<span class="keyword"> const</span>{</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  </div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  T tmp = 0;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;tmp += std::pow(<a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i],2);</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  }</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="keywordflow">return</span> std::sqrt(tmp);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  </div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;}</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment"> * Primary Tensor template class</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment"> * @tparam order An unsigned int defining the order of the tensor (1, 2, 3, or 4).</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment"> * @tparam dim An unsigned int defing the spatial dimension of the problem.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment"> * @tparam T The type that is to be stored in the tensor.</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <span class="keyword">class </span><a class="code" href="class_tensor.html">Tensor</a>{</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  <a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor</a>();</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;b);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment"> * Access/set an element of the tensor. Returns a tensor with the order reduced by 1.</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"><a class="line" href="class_tensor.html#a2a730307c55f50e6a9d3665c234620e6">   94</a></span>&#160;  <a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,T&gt;&amp; <a class="code" href="class_tensor.html#a2a730307c55f50e6a9d3665c234620e6">operator[]</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i){ <span class="keywordflow">return</span> <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i]; };</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment"> * Access an element of the tensor. Returns a tensor with the order reduced by 1.</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="class_tensor.html#a9688ac9421205322f94c72d7cf6e7595">   99</a></span>&#160;  <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,T&gt;&amp; <a class="code" href="class_tensor.html#a9688ac9421205322f94c72d7cf6e7595">operator[]</a>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i]; };</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a>&amp; <a class="code" href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">operator=</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;b);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> U&gt; <span class="keyword">auto</span> <a class="code" href="class_tensor.html#aff0f9e2b08f25ed6af07cd81a0ed6676">operator*</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;1,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;())&gt; <span class="keyword">const</span>;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  </div>
<div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">  103</a></span>&#160;  std::vector&lt;<a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,T&gt; &gt; <a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;};</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment"> * Default constructor.</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">  110</a></span>&#160;<a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor&lt;order,dim,T&gt;::Tensor</a>() : value(dim){}</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="comment"> * Copy constructor.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="class_tensor.html#a0528c8f5592468e7bc7c78fcb843712b">  116</a></span>&#160;<a class="code" href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor&lt;order,dim,T&gt;::Tensor</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;b){</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  *<span class="keyword">this</span> = b;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;}</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment"> * Assignment operator.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">  126</a></span>&#160;<a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a>&amp; <a class="code" href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">Tensor&lt;order,dim,T&gt;::operator=</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;b){</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  </div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  value = b.<a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;}</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment"> * Contract the given tensor with a 1st order tensor.</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> U&gt;</div>
<div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="class_tensor.html#aff0f9e2b08f25ed6af07cd81a0ed6676">  138</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#aff0f9e2b08f25ed6af07cd81a0ed6676">Tensor&lt;order,dim,T&gt;::operator*</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;1,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;())&gt; <span class="keyword">const</span>{</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  <a class="code" href="class_tensor.html">Tensor</a>&lt;order-1,dim,decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    tmp[i] = this-&gt;value[i]*b;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  }</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;}</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment"> * @name Operations related to all Tensor objects:</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment"> * Scalar multiplication of a Tensor, where the scalar precedes the Tensor object.</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt; </div>
<div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="class_tensor.html#a13e72a006d63e8af09966686b9251da7">  159</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a13e72a006d63e8af09966686b9251da7">operator*</a>(T a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  </div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;      tmp[i] = a*b[i];</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  }</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;}</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment"> * Scalar multiplication of a Tensor, where the scalar follows the Tensor object.</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt; </div>
<div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="class_tensor.html#a245f6c779208e2fb51aeac547f1c5fce">  176</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a245f6c779208e2fb51aeac547f1c5fce">operator*</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,U&gt;</a> &amp;b,T a) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;  </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      tmp[i] = a*b[i];</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  </div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;}</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment"> * Addition operator for any two Tensors of the same order.</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt; </div>
<div class="line"><a name="l00193"></a><span class="lineno"><a class="line" href="class_tensor.html#a07fcde25f086faf2afb1d80d402ee694">  193</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a07fcde25f086faf2afb1d80d402ee694">operator+</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()+std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()+std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;      tmp[i] = a[i]+b[i];</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  }</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;}</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment"> * Subtraction operator for any two Tensors of the same order.</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> order,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt; </div>
<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="class_tensor.html#a8ebb19fbf586d07e5a4c6cefac26cb5d">  210</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a8ebb19fbf586d07e5a4c6cefac26cb5d">operator-</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;order,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()-std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  </div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;order,dim,decltype(std::declval&lt;T&gt;</a>()-std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;      tmp[i] = a[i]-b[i];</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  }</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  </div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;}</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;<span class="comment"> * @name Operations related to 1st order Tensor objects:</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;<span class="comment"> * Single contraction (i.e. dot product) of two 1st order Tensor objects. Returns a scalar.</span></div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt; </div>
<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="class_tensor.html#a3e99a15f8a8467028028b8d60e8fc580">  231</a></span>&#160;<span class="keyword">auto</span> <a class="code" href="class_tensor.html#a3e99a15f8a8467028028b8d60e8fc580">operator*</a>(<span class="keyword">const</span> <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;1,dim,U&gt;</a> &amp;b) -&gt; decltype(a[0]*b[0]){</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  decltype(a[0]*b[0]) tmp(0);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    tmp += a[i]*b[i];</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  }</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  </div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;}</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;<span class="comment"> * @name Operations related to 2nd order Tensor objects:</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;<span class="comment"> * Double contraction of two 2nd order Tensor objects. Returns a scalar.</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt;</div>
<div class="line"><a name="l00252"></a><span class="lineno"><a class="line" href="class_tensor.html#a5a8bda2f027340305afc45b49388bcc8">  252</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a5a8bda2f027340305afc45b49388bcc8">double_contract</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,U&gt;</a> &amp;b) -&gt; decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()){</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  </div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()) tmp = 0;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;      tmp += a[i][j]*b[i][j];</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    }</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  }</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  </div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;}</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="comment"> * Multiplication operator of two 2nd order Tensor objects (equivalent to matrix multiplication). Returns a 2nd order Tensor object.</span></div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt;</div>
<div class="line"><a name="l00271"></a><span class="lineno"><a class="line" href="class_tensor.html#a8fc3d16cc82edd3a5d4c40f20863bb91">  271</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a8fc3d16cc82edd3a5d4c40f20863bb91">operator*</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;2,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;dim; ++k){</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    tmp[i][k] += a[i][j]*b[j][k];</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;      }</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    }</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  }</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  </div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  </div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;}</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;<span class="comment"> * Converts the 2nd order Tensor object to an isotropic tensor (equivalent to the identity matrix).</span></div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00292"></a><span class="lineno"><a class="line" href="class_tensor.html#ad82bf064ac85d03cde37854363afe9de">  292</a></span>&#160;  <span class="keywordtype">void</span> <a class="code" href="class_tensor.html#ad82bf064ac85d03cde37854363afe9de">identity</a>(<a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  </div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;      a[i][j] = (i == j);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    }</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  }</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;}</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="comment"> * Returns the transpose of the 2nd order Tensor object.</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00307"></a><span class="lineno"><a class="line" href="class_tensor.html#ae47b0b29069a6f95a8ea98c64b6d91e8">  307</a></span>&#160;<a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> <a class="code" href="class_tensor.html#ae47b0b29069a6f95a8ea98c64b6d91e8">trans</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> tmp;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;      tmp[i][j] = a[j][i];</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    }</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  }</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;}</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="comment"> * Returns the trace of the 2nd order Tensor object.</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00325"></a><span class="lineno"><a class="line" href="class_tensor.html#aa49dbdc74bfc6fba3f707032e4918b7c">  325</a></span>&#160;T <a class="code" href="class_tensor.html#aa49dbdc74bfc6fba3f707032e4918b7c">trace</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;  T tmp(0);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    tmp += a[i][i];</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  }</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;}</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="comment"> * Returns the determinant of the 2nd order Tensor object (dim==2).</span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00341"></a><span class="lineno"><a class="line" href="class_tensor.html#a4d1f4671cbc87300dbbb987b6db28d96">  341</a></span>&#160;T <a class="code" href="class_tensor.html#a4d1f4671cbc87300dbbb987b6db28d96">det</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,2,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  </div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="keywordflow">return</span> (a[0][0]*a[1][1] - a[0][1]*a[1][0]);</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;}</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;<span class="comment"> * Returns the determinant of the 2nd order Tensor object (dim==3).</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00352"></a><span class="lineno"><a class="line" href="class_tensor.html#a7843bbc36c9300509f6cefb1c1ebf64f">  352</a></span>&#160;T <a class="code" href="class_tensor.html#a7843bbc36c9300509f6cefb1c1ebf64f">det</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,3,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  </div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="keywordflow">return</span> (a[0][0]*(a[1][1]*a[2][2] - a[1][2]*a[2][1])</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      - a[0][1]*(a[1][0]*a[2][2] - a[1][2]*a[2][0])</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;      + a[0][2]*(a[1][0]*a[2][1] - a[1][1]*a[2][0]));</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;}</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;<span class="comment"> * Returns the inverse of the 2nd order Tensor object (dim==2).</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00365"></a><span class="lineno"><a class="line" href="class_tensor.html#a8ed527cd06f7c6169e944b6332e81a44">  365</a></span>&#160;<a class="code" href="class_tensor.html">Tensor&lt;2,2,T&gt;</a> <a class="code" href="class_tensor.html#a8ed527cd06f7c6169e944b6332e81a44">inv</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,2,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    </div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  T J = <a class="code" href="class_tensor.html#a4d1f4671cbc87300dbbb987b6db28d96">det</a>(a);</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,2,T&gt;</a> tmp;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  tmp[0][0] = 1./J*a[1][1];</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  tmp[0][1] = -1./J*a[0][1];</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  tmp[1][0] = -1./J*a[1][0];</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  tmp[1][1] = 1./J*a[0][0];</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;}</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="comment"> * Returns the inverse of the 2nd order Tensor object (dim==3).</span></div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00383"></a><span class="lineno"><a class="line" href="class_tensor.html#a27d9a099d122fe2525805ba60f5ff6fe">  383</a></span>&#160;<a class="code" href="class_tensor.html">Tensor&lt;2,3,T&gt;</a> <a class="code" href="class_tensor.html#a27d9a099d122fe2525805ba60f5ff6fe">inv</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,3,T&gt;</a>&amp; a) {</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    </div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  T J = <a class="code" href="class_tensor.html#a4d1f4671cbc87300dbbb987b6db28d96">det</a>(a);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,3,T&gt;</a> tmp;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  tmp[0][0] = 1./J*(a[1][1]*a[2][2] - a[2][1]*a[1][2]);</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;  tmp[0][1] = 1./J*(a[0][2]*a[2][1] - a[0][1]*a[2][2]);</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  tmp[0][2] = 1./J*(a[0][1]*a[1][2] - a[1][1]*a[0][2]);</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  tmp[1][0] = 1./J*(a[1][2]*a[2][0] - a[2][2]*a[1][0]);</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  tmp[1][1] = 1./J*(a[0][0]*a[2][2] - a[2][0]*a[0][2]);</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;  tmp[1][2] = 1./J*(a[0][2]*a[1][0] - a[1][2]*a[0][0]);</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  tmp[2][0] = 1./J*(a[1][0]*a[2][1] - a[2][0]*a[1][1]);</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  tmp[2][1] = 1./J*(a[0][1]*a[2][0] - a[2][1]*a[0][0]);</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  tmp[2][2] = 1./J*(a[0][0]*a[1][1] - a[1][0]*a[0][1]);</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;}</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="comment"> * @name Operations related to 3rd order Tensor objects:</span></div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="comment"> * Triple contraction of two 3rd order Tensor objects. Returns a scalar.</span></div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt;</div>
<div class="line"><a name="l00410"></a><span class="lineno"><a class="line" href="class_tensor.html#a0d8d7cd689342c88f61442873c060b89">  410</a></span>&#160;  <span class="keyword">auto</span> <a class="code" href="class_tensor.html#a0d8d7cd689342c88f61442873c060b89">triple_contract</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;3,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;3,dim,U&gt;</a> &amp;b) -&gt; decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()){</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  </div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()) tmp = 0;</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;dim; ++k){</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    tmp += a[i][j][k]*b[i][j][k];</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;      }</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    }</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  }</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  </div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  </div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;}</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;<span class="comment"> * @name Operations related to 4th order Tensor objects:</span></div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;<span class="comment"> * Performs a full contraction on two 2nd order Tensors, \f$a\f$ and \f$c\f$, and a 4th order Tensor, \f$b\f$, in this manner: \f$a_{ij}b_{ijkl}c_{kl}\f$,</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;<span class="comment"> * with implied summation over all indices. Returns a scalar.</span></div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U,<span class="keyword">typename</span> V&gt;</div>
<div class="line"><a name="l00436"></a><span class="lineno"><a class="line" href="class_tensor.html#ab50f9741f15a2b5891037f70c5598ae1">  436</a></span>&#160;<span class="keyword">auto</span> <a class="code" href="class_tensor.html#ab50f9741f15a2b5891037f70c5598ae1">full_contract</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;4,dim,U&gt;</a> &amp;b, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,V&gt;</a> &amp;c) -&gt; decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()*std::declval&lt;V&gt;()){</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  </div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  decltype(std::declval&lt;T&gt;()*std::declval&lt;U&gt;()*std::declval&lt;V&gt;()) tmp = 0;</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;dim; ++k){</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> l=0; l&lt;dim; ++l){</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;      tmp += a[i][j]*b[i][j][k][l]*c[k][l];</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    }</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;      }</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    }</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  }</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  </div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  </div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;}</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;<span class="comment"> * Performs a double contraction between a 4th order Tensor, \f$a\f$, and a 2nd order Tensor, \f$b\f$, in this manner: \f$a_{ijkl}b_{kl}\f$,</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;<span class="comment"> * with implied summation over \f$k\f$ and \f$l\f$.</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T,<span class="keyword">typename</span> U&gt;</div>
<div class="line"><a name="l00460"></a><span class="lineno"><a class="line" href="class_tensor.html#adce659b434eae62cf38d6d54afb6abcf">  460</a></span>&#160;<span class="keyword">auto</span> <a class="code" href="class_tensor.html#adce659b434eae62cf38d6d54afb6abcf">double_contract</a>(<span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;4,dim,T&gt;</a> &amp;a, <span class="keyword">const</span> <a class="code" href="class_tensor.html">Tensor&lt;2,dim,U&gt;</a> &amp;b) -&gt; <a class="code" href="class_tensor.html">Tensor&lt;2,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt;{</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  </div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,dim,decltype(std::declval&lt;T&gt;</a>()*std::declval&lt;U&gt;())&gt; tmp;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j=0; j&lt;dim; ++j){</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;      tmp[i][j] = 0;</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k=0; k&lt;dim; ++k){</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> l=0; l&lt;dim; ++l){</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;      tmp[i][j] += a[i][j][k][l]*b[k][l];</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    }</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;      }</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    }</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;  }</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  </div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  </div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;}</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;<span class="comment"> * @name Operations converting arrays to Tensor objects:</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;<span class="comment"> * Converts 1D array to a 1st order Tensor</span></div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00488"></a><span class="lineno"><a class="line" href="class_tensor.html#a006cda52416d4282f3eb209dfb96c9e2">  488</a></span>&#160;  <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> <a class="code" href="class_tensor.html#a006cda52416d4282f3eb209dfb96c9e2">convert</a>(<span class="keyword">const</span> T b[]){</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  <a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt;1,dim,T&gt;</a> tmp;</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  tmp.<a class="code" href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aec326c324745d11291d2f0d5d7eea804">value</a>.assign(b,b+dim);</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  </div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;}</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;<span class="comment"> * Converts 2D array to a 2nd order Tensor</span></div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00502"></a><span class="lineno"><a class="line" href="class_tensor.html#a7ff5a91439f88fd82aed50dafb31bdb5">  502</a></span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> <a class="code" href="class_tensor.html#a7ff5a91439f88fd82aed50dafb31bdb5">convert</a>(<span class="keyword">const</span> T b[][dim]){</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  </div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;2,dim,T&gt;</a> tmp;</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    tmp.<a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i] = convert&lt;dim,T&gt;(b[i]);</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  }</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  </div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;}</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;<span class="comment"> * Converts 3D array to a 3rd order Tensor</span></div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00518"></a><span class="lineno"><a class="line" href="class_tensor.html#a87bd0388317717327d40d91664ed4c5c">  518</a></span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;3,dim,T&gt;</a> <a class="code" href="class_tensor.html#a87bd0388317717327d40d91664ed4c5c">convert</a>(<span class="keyword">const</span> T b[][dim][dim]){</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  </div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;3,dim,T&gt;</a> tmp;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    tmp.<a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i] = convert&lt;dim,T&gt;(b[i]);</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  }</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  </div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;}</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;<span class="comment"> * @relates Tensor</span></div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;<span class="comment"> * </span></div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;<span class="comment"> * Converts 4D array to a 4th order Tensor</span></div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dim,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00534"></a><span class="lineno"><a class="line" href="class_tensor.html#ac33df3d5766648f68fa66739df2f639e">  534</a></span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;4,dim,T&gt;</a> <a class="code" href="class_tensor.html#ac33df3d5766648f68fa66739df2f639e">convert</a>(<span class="keyword">const</span> T b[][dim][dim][dim]){</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;  </div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  <a class="code" href="class_tensor.html">Tensor&lt;4,dim,T&gt;</a> tmp;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;  <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;dim; ++i){</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    tmp.<a class="code" href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">value</a>[i] = convert&lt;dim,T&gt;(b[i]);</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;  }</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  </div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  <span class="keywordflow">return</span> tmp;</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;}</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;<span class="preprocessor">#endif //TENSOR_H</span></div>
<div class="ttc" id="class_tensor_html_adce659b434eae62cf38d6d54afb6abcf"><div class="ttname"><a href="class_tensor.html#adce659b434eae62cf38d6d54afb6abcf">Tensor::double_contract</a></div><div class="ttdeci">auto double_contract(const Tensor&lt; 4, dim, T &gt; &amp;a, const Tensor&lt; 2, dim, U &gt; &amp;b) -&gt; Tensor&lt; 2, dim, decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:460</div></div>
<div class="ttc" id="class_tensor_html_a5a8bda2f027340305afc45b49388bcc8"><div class="ttname"><a href="class_tensor.html#a5a8bda2f027340305afc45b49388bcc8">Tensor::double_contract</a></div><div class="ttdeci">auto double_contract(const Tensor&lt; 2, dim, T &gt; &amp;a, const Tensor&lt; 2, dim, U &gt; &amp;b) -&gt; decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())</div><div class="ttdef"><b>Definition:</b> tensor.h:252</div></div>
<div class="ttc" id="class_tensor_html_a7ff5a91439f88fd82aed50dafb31bdb5"><div class="ttname"><a href="class_tensor.html#a7ff5a91439f88fd82aed50dafb31bdb5">Tensor::convert</a></div><div class="ttdeci">Tensor&lt; 2, dim, T &gt; convert(const T b[][dim])</div><div class="ttdef"><b>Definition:</b> tensor.h:502</div></div>
<div class="ttc" id="class_tensor_html_ab50f9741f15a2b5891037f70c5598ae1"><div class="ttname"><a href="class_tensor.html#ab50f9741f15a2b5891037f70c5598ae1">Tensor::full_contract</a></div><div class="ttdeci">auto full_contract(const Tensor&lt; 2, dim, T &gt; &amp;a, const Tensor&lt; 4, dim, U &gt; &amp;b, const Tensor&lt; 2, dim, V &gt; &amp;c) -&gt; decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;()*std::declval&lt; V &gt;())</div><div class="ttdef"><b>Definition:</b> tensor.h:436</div></div>
<div class="ttc" id="class_tensor_html_a07fcde25f086faf2afb1d80d402ee694"><div class="ttname"><a href="class_tensor.html#a07fcde25f086faf2afb1d80d402ee694">Tensor::operator+</a></div><div class="ttdeci">auto operator+(const Tensor&lt; order, dim, T &gt; &amp;a, const Tensor&lt; order, dim, U &gt; &amp;b) -&gt; Tensor&lt; order, dim, decltype(std::declval&lt; T &gt;()+std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:193</div></div>
<div class="ttc" id="class_tensor_html_a9688ac9421205322f94c72d7cf6e7595"><div class="ttname"><a href="class_tensor.html#a9688ac9421205322f94c72d7cf6e7595">Tensor::operator[]</a></div><div class="ttdeci">const Tensor&lt; order-1, dim, T &gt; &amp; operator[](unsigned int i) const </div><div class="ttdef"><b>Definition:</b> tensor.h:99</div></div>
<div class="ttc" id="class_tensor_html_ac33df3d5766648f68fa66739df2f639e"><div class="ttname"><a href="class_tensor.html#ac33df3d5766648f68fa66739df2f639e">Tensor::convert</a></div><div class="ttdeci">Tensor&lt; 4, dim, T &gt; convert(const T b[][dim][dim][dim])</div><div class="ttdef"><b>Definition:</b> tensor.h:534</div></div>
<div class="ttc" id="class_tensor_html_a7843bbc36c9300509f6cefb1c1ebf64f"><div class="ttname"><a href="class_tensor.html#a7843bbc36c9300509f6cefb1c1ebf64f">Tensor::det</a></div><div class="ttdeci">T det(const Tensor&lt; 2, 3, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:352</div></div>
<div class="ttc" id="class_tensor_html_a3e99a15f8a8467028028b8d60e8fc580"><div class="ttname"><a href="class_tensor.html#a3e99a15f8a8467028028b8d60e8fc580">Tensor::operator*</a></div><div class="ttdeci">auto operator*(const Tensor&lt; 1, dim, T &gt; &amp;a, const Tensor&lt; 1, dim, U &gt; &amp;b) -&gt; decltype(a[0]*b[0])</div><div class="ttdef"><b>Definition:</b> tensor.h:231</div></div>
<div class="ttc" id="class_tensor_html_a13e72a006d63e8af09966686b9251da7"><div class="ttname"><a href="class_tensor.html#a13e72a006d63e8af09966686b9251da7">Tensor::operator*</a></div><div class="ttdeci">auto operator*(T a, const Tensor&lt; order, dim, U &gt; &amp;b) -&gt; Tensor&lt; order, dim, decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:159</div></div>
<div class="ttc" id="class_tensor_html_a09dacbd79d16b74ba8698e27ae3dc42b"><div class="ttname"><a href="class_tensor.html#a09dacbd79d16b74ba8698e27ae3dc42b">Tensor::Tensor</a></div><div class="ttdeci">Tensor()</div><div class="ttdef"><b>Definition:</b> tensor.h:110</div></div>
<div class="ttc" id="class_tensor_html_a5f0bed513e88b3d46634d64d0728d7eb"><div class="ttname"><a href="class_tensor.html#a5f0bed513e88b3d46634d64d0728d7eb">Tensor::operator=</a></div><div class="ttdeci">Tensor&lt; order, dim, T &gt; &amp; operator=(const Tensor&lt; order, dim, T &gt; &amp;b)</div><div class="ttdef"><b>Definition:</b> tensor.h:126</div></div>
<div class="ttc" id="class_tensor_3_011_00_01dim_00_01_t_01_4_html_aec326c324745d11291d2f0d5d7eea804"><div class="ttname"><a href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#aec326c324745d11291d2f0d5d7eea804">Tensor&lt; 1, dim, T &gt;::value</a></div><div class="ttdeci">std::vector&lt; T &gt; value</div><div class="ttdef"><b>Definition:</b> tensor.h:34</div></div>
<div class="ttc" id="class_tensor_html_a8fc3d16cc82edd3a5d4c40f20863bb91"><div class="ttname"><a href="class_tensor.html#a8fc3d16cc82edd3a5d4c40f20863bb91">Tensor::operator*</a></div><div class="ttdeci">auto operator*(const Tensor&lt; 2, dim, T &gt; a, const Tensor&lt; 2, dim, U &gt; &amp;b) -&gt; Tensor&lt; 2, dim, decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:271</div></div>
<div class="ttc" id="class_tensor_html_a006cda52416d4282f3eb209dfb96c9e2"><div class="ttname"><a href="class_tensor.html#a006cda52416d4282f3eb209dfb96c9e2">Tensor::convert</a></div><div class="ttdeci">Tensor&lt; 1, dim, T &gt; convert(const T b[])</div><div class="ttdef"><b>Definition:</b> tensor.h:488</div></div>
<div class="ttc" id="class_tensor_html_a0d8d7cd689342c88f61442873c060b89"><div class="ttname"><a href="class_tensor.html#a0d8d7cd689342c88f61442873c060b89">Tensor::triple_contract</a></div><div class="ttdeci">auto triple_contract(const Tensor&lt; 3, dim, T &gt; &amp;a, const Tensor&lt; 3, dim, U &gt; &amp;b) -&gt; decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())</div><div class="ttdef"><b>Definition:</b> tensor.h:410</div></div>
<div class="ttc" id="class_tensor_html_ad82bf064ac85d03cde37854363afe9de"><div class="ttname"><a href="class_tensor.html#ad82bf064ac85d03cde37854363afe9de">Tensor::identity</a></div><div class="ttdeci">void identity(Tensor&lt; 2, dim, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:292</div></div>
<div class="ttc" id="class_tensor_html"><div class="ttname"><a href="class_tensor.html">Tensor</a></div><div class="ttdef"><b>Definition:</b> tensor.h:10</div></div>
<div class="ttc" id="class_tensor_html_a4d1f4671cbc87300dbbb987b6db28d96"><div class="ttname"><a href="class_tensor.html#a4d1f4671cbc87300dbbb987b6db28d96">Tensor::det</a></div><div class="ttdeci">T det(const Tensor&lt; 2, 2, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:341</div></div>
<div class="ttc" id="class_tensor_3_011_00_01dim_00_01_t_01_4_html_acc931891ae9e3bb537e3a0a78ff87d8f"><div class="ttname"><a href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#acc931891ae9e3bb537e3a0a78ff87d8f">Tensor&lt; 1, dim, T &gt;::operator[]</a></div><div class="ttdeci">T &amp; operator[](unsigned int i)</div><div class="ttdef"><b>Definition:</b> tensor.h:25</div></div>
<div class="ttc" id="class_tensor_html_aff0f9e2b08f25ed6af07cd81a0ed6676"><div class="ttname"><a href="class_tensor.html#aff0f9e2b08f25ed6af07cd81a0ed6676">Tensor::operator*</a></div><div class="ttdeci">auto operator*(const Tensor&lt; 1, dim, U &gt; &amp;b) -&gt; Tensor&lt; order-1, dim, decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())&gt; const</div><div class="ttdef"><b>Definition:</b> tensor.h:138</div></div>
<div class="ttc" id="class_tensor_html_ae47b0b29069a6f95a8ea98c64b6d91e8"><div class="ttname"><a href="class_tensor.html#ae47b0b29069a6f95a8ea98c64b6d91e8">Tensor::trans</a></div><div class="ttdeci">Tensor&lt; 2, dim, T &gt; trans(const Tensor&lt; 2, dim, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:307</div></div>
<div class="ttc" id="class_tensor_html_a245f6c779208e2fb51aeac547f1c5fce"><div class="ttname"><a href="class_tensor.html#a245f6c779208e2fb51aeac547f1c5fce">Tensor::operator*</a></div><div class="ttdeci">auto operator*(const Tensor&lt; order, dim, U &gt; &amp;b, T a) -&gt; Tensor&lt; order, dim, decltype(std::declval&lt; T &gt;()*std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:176</div></div>
<div class="ttc" id="class_tensor_html_aa49dbdc74bfc6fba3f707032e4918b7c"><div class="ttname"><a href="class_tensor.html#aa49dbdc74bfc6fba3f707032e4918b7c">Tensor::trace</a></div><div class="ttdeci">T trace(const Tensor&lt; 2, dim, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:325</div></div>
<div class="ttc" id="class_tensor_html_a8ebb19fbf586d07e5a4c6cefac26cb5d"><div class="ttname"><a href="class_tensor.html#a8ebb19fbf586d07e5a4c6cefac26cb5d">Tensor::operator-</a></div><div class="ttdeci">auto operator-(const Tensor&lt; order, dim, T &gt; &amp;a, const Tensor&lt; order, dim, U &gt; &amp;b) -&gt; Tensor&lt; order, dim, decltype(std::declval&lt; T &gt;()-std::declval&lt; U &gt;())&gt;</div><div class="ttdef"><b>Definition:</b> tensor.h:210</div></div>
<div class="ttc" id="class_tensor_3_011_00_01dim_00_01_t_01_4_html_a326179f24c05ffe25beedd71ff0f23b1"><div class="ttname"><a href="class_tensor_3_011_00_01dim_00_01_t_01_4.html#a326179f24c05ffe25beedd71ff0f23b1">Tensor&lt; 1, dim, T &gt;::operator[]</a></div><div class="ttdeci">const T &amp; operator[](unsigned int i) const </div><div class="ttdef"><b>Definition:</b> tensor.h:30</div></div>
<div class="ttc" id="class_tensor_html_a2a730307c55f50e6a9d3665c234620e6"><div class="ttname"><a href="class_tensor.html#a2a730307c55f50e6a9d3665c234620e6">Tensor::operator[]</a></div><div class="ttdeci">Tensor&lt; order-1, dim, T &gt; &amp; operator[](unsigned int i)</div><div class="ttdef"><b>Definition:</b> tensor.h:94</div></div>
<div class="ttc" id="class_tensor_html_a27d9a099d122fe2525805ba60f5ff6fe"><div class="ttname"><a href="class_tensor.html#a27d9a099d122fe2525805ba60f5ff6fe">Tensor::inv</a></div><div class="ttdeci">Tensor&lt; 2, 3, T &gt; inv(const Tensor&lt; 2, 3, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:383</div></div>
<div class="ttc" id="class_tensor_html_a1b0f8dc1dc255e5d031bf1ec123793ee"><div class="ttname"><a href="class_tensor.html#a1b0f8dc1dc255e5d031bf1ec123793ee">Tensor::value</a></div><div class="ttdeci">std::vector&lt; Tensor&lt; order-1, dim, T &gt; &gt; value</div><div class="ttdef"><b>Definition:</b> tensor.h:103</div></div>
<div class="ttc" id="class_tensor_html_a8ed527cd06f7c6169e944b6332e81a44"><div class="ttname"><a href="class_tensor.html#a8ed527cd06f7c6169e944b6332e81a44">Tensor::inv</a></div><div class="ttdeci">Tensor&lt; 2, 2, T &gt; inv(const Tensor&lt; 2, 2, T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> tensor.h:365</div></div>
<div class="ttc" id="class_tensor_3_011_00_01dim_00_01_t_01_4_html"><div class="ttname"><a href="class_tensor_3_011_00_01dim_00_01_t_01_4.html">Tensor&lt; 1, dim, T &gt;</a></div><div class="ttdef"><b>Definition:</b> tensor.h:17</div></div>
<div class="ttc" id="class_tensor_html_a87bd0388317717327d40d91664ed4c5c"><div class="ttname"><a href="class_tensor.html#a87bd0388317717327d40d91664ed4c5c">Tensor::convert</a></div><div class="ttdeci">Tensor&lt; 3, dim, T &gt; convert(const T b[][dim][dim])</div><div class="ttdef"><b>Definition:</b> tensor.h:518</div></div>
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